# How do you find the equation of the line that passes through the point (0,2) and perpendicular to the line x-y=6?

Mar 4, 2018

$x + y = 2$

#### Explanation:

let,the equation of the line be $y = m x + c$ where, $m$ is the slope and $c$ is the $Y$ intercept.

now,slope of the equation $x - y = 6$ or $y = x - 6$ is $1$

We know that for two lines to be mutually perpendicular,their product of slope will have to be $- 1$

So,$m \cdot 1 = - 1$

or, $m = - 1$

So,the equation becomes, $y = - x + c$

Now,given the line passes through $\left(0 , 2\right)$

So,putting the values we get,

$2 = 0 + c$

So,the equation of the line is, $y = - x + 2$

or, $x + y = 2$ graph{x+y=2 [-10, 10, -5, 5]}